SomehowI suspect that you are expecting too much in the way of accuracy from your lathe.
Initially, you set off with problems with stiff handles or dials and came up with a question about the fit of a pair of sliding parts- and then came up with a solution of - Using grease! Sorry but the correct lubricant for sliding parts is slideways oil or even ordinary motor oil-- but not grease.
Again, you did this 'improvement' with the feed screws. Sorry, the slides are always done by removing the feed screws, oiling and feeling them slide - to suit your way of working. Then, the feed screws and nuts are replaced- and tested again for stiffness, backlash and so on.
If, as others and yourself mentioned, there was some doubt about fit and 'faked' scraping, you should have blued the matting parts in- and got a scraper out and got them to fit. You may have had to scrape the gibs or even had to peg them- but you would have a nicely adjusted lathe.
This would have given you a lathe which would be nice to quickly clean at each maintenance session. Because this is what everyone has to do-- or should do!
Let us turn to three jaw chucks now. Few lathes possess chucks which are really accurate. You can expect them to hold perhaps 0.003" TIR but to get better, you involve greater expense in having to get something like a Griptru. If you cannot afford one, then you use a independent four jaw or perhaps collets if the work is small enough.
Now, you have some difficulty in fitting retro-fitting a three jaw backplate. Initially, the backplate should be machined to get an accurate face and then addressed to take new chuck. As the chuck is going to have an element of inaccuracy, you should clock - not on the jaws but on the outside of the chuck body- and after all the mechanism has been removed- and everything ready and cleaned. The bolt holes or tappings follow and only after the lot has been de-burred, assembled.
As far as the collets are concerned, you only get what you pay for.
Above all, you should check your own work- step by step- and make each correction and adjustment as you go along.
I have no doubt that others will find room to criticise these comments but it should suffice to say that I run an very old Myford Super 7 which had been abused and used on woodwork. The bed was re-ground professionally and the fit of the saddle had to be re-built with Turcite.
The smaller items were scraped in by hand and the things like broken and sheared gears were machined and fitted.
Unashamedly, this is not perfect and some parts could do with replacing but there is always difficulty in getting spares- or finding time to make them.
I hope that my comments might be of some use to you.
